CN108196200B - Combined simulation evaluation method for health and state of charge of lithium battery - Google Patents

Combined simulation evaluation method for health and state of charge of lithium battery Download PDF

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CN108196200B
CN108196200B CN201810080690.4A CN201810080690A CN108196200B CN 108196200 B CN108196200 B CN 108196200B CN 201810080690 A CN201810080690 A CN 201810080690A CN 108196200 B CN108196200 B CN 108196200B
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朱丽群
李旦
张建秋
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Fudan University
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    • G01—MEASURING; TESTING
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    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
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    • G—PHYSICS
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    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
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Abstract

The invention belongs to the technical field of lithium battery health management, and particularly relates to a joint simulation evaluation method for lithium battery health and state of charge. The method utilizes the equivalent circuit of the lithium battery to describe the characteristics of the battery, and provides a description means for hysteresis phenomenon existing in the relation between open-circuit voltage and state of charge; the internal resistance of the battery is introduced as a state variable and is associated with the battery health state defined from the aspects of the battery capacity and the internal resistance, so that the current capacity of the battery is updated in real time by updating the internal resistance, and the aging of the battery can be adapted to keep high description precision all the time. Compared with the prior art, the method can realize real-time online capacity estimation which is difficult to realize by the traditional method, ensure the real-time accuracy of the circuit equivalent model and provide reference for the health state and the charge state of the battery.

Description

Combined simulation evaluation method for health and state of charge of lithium battery
Technical Field
The invention belongs to the technical field of lithium battery health management, and particularly relates to a joint simulation evaluation method for lithium battery health and state of charge.
Background
The lithium ion battery has the advantages of high energy density, low self-discharge rate, long service life and the like, so that the lithium ion battery is more and more widely applied to the fields of mobile electronic equipment, power automobiles and the like. But these advantages are only guaranteed in a safe operating environment. Therefore, in order to ensure that the lithium battery can work in such an operating environment, the battery needs to be managed. On-line estimation of the internal state of the lithium battery is a precondition for battery management. The internal State of a lithium battery mainly refers to its State of Charge (SOC) and State of Health (SOH). The former is used to indicate the current remaining capacity of the battery, and the latter is used to describe the attenuation degree of the maximum dischargeable capacity of the battery.
The SOC is defined as the ratio of the remaining battery capacity to the full battery capacity. In the battery management module, in order to prevent the overcharge and overdischarge of the battery, the charge and discharge current thereof needs to be controlled by using the SOC information, so accurate SOC estimation is of great practical significance. However, the SOC cannot be directly obtained by measurement, and can only be estimated by some method[1]. At present, the following four main estimation methods for SOCThe method comprises the following steps: 1) ampere-hour integration, which estimates SOC by integrating the current flowing into/out of the battery, has an error that is inevitably present in any open-loop prediction method, and thus its estimation results are continuously accumulated with an increase in the integration time. In addition, the estimation needs to be performed in advance with an accurate initial value of SOC, which brings difficulty to the practical application thereof[2](ii) a 2) The Open circuit voltage method obtains an SOC estimation value using a correspondence between Open Circuit Voltage (OCV) and SOC, but such a correspondence requires a long time for the battery to be stationary and cannot be used for real-time estimation[3](ii) a 3) The internal resistance method can be carried out only by a high-precision measuring instrument, so that the method is not suitable for a scene of real-time work[4](ii) a 4) An equivalent circuit model method for describing the battery by constructing an equivalent circuit model based on the current-voltage relationship between two ends of the battery, i.e. expressing the charge-discharge characteristics of the battery by using a circuit equation[5～6]。
At present, the most common battery estimation methods are all estimation methods based on battery equivalent circuit models[1]. Document [7]]A common equivalent circuit model is introduced, and because the model simulates the charge and discharge characteristics of the battery by using corresponding circuit elements, the element parameters can be determined according to the charge and discharge voltage and current of the battery. Based on the equivalent circuit models, corresponding state equations can be constructed, and based on the state equations, people can utilize a Kalman filter[5]Or sliding mode observer[6]And the like to estimate the required battery parameters in real time. Although such models can better simulate the charge and discharge characteristics of the battery, they have some problems. On the one hand, in such models, it is generally assumed that the OCV-SOC correspondence relationship is fixed during charge and discharge, and document [8 ]][9]The study of (a) shows that: the corresponding relation between the OCV and the SOC has hysteresis phenomenon in the charging and discharging process of the battery, which is specifically represented as follows: in the same SOC state, the OCV is deviated due to different charge and discharge states of the battery at the previous time. This indicates that such equivalent circuit model has model errors. On the other hand, as the battery is discharged to a very small SOC stateThe internal resistance of the lithium battery increases exponentially. In addition, as the attenuation of the battery ages, the internal resistance of the battery increases, and the capacity of the battery decreases. This variation cannot be represented by a constant resistance and a constant capacitance in the equivalent circuit model, which means that the model error for estimation thereof becomes large in an extremely small SOC state or after degradation of battery degradation, resulting in a decrease in estimation accuracy.
The battery capacity refers to the maximum dischargeable electric quantity of the battery in the current state, and the attenuation condition of the battery can be represented by battery SOH. There are fewer studies reported to correlate with SOH relative to SOC studies. Document [10] proposes an empirical cycle life model of a lithium ion battery, but the model takes into account many physical factors of the battery, and therefore cannot be well adapted to different batteries; similarly, document [11] also gives a mathematical model of capacity fading of the lithium ion battery, but the model is an empirical model, and the model has uncertainty for different batteries and is not suitable for practical application scenarios.
Aiming at the problems of the battery state-of-charge estimation and the state-of-health estimation, the invention introduces a battery equivalent model proposed by the document [7] into a time-varying internal resistance, and is characterized by introducing white Gaussian noise into a hysteresis phenomenon existing in an open-circuit voltage and state-of-charge relation curve in order to describe the uncertainty existing in the curve. The internal resistance as a state variable is correlated with the state of health of the battery, thereby providing a new way of estimating the capacity of the battery. Thus we have built a new model for battery state of charge estimation and state of health estimation. Analysis shows that: the model can describe the possible change of the corresponding relation between the SOC and the OCV of the battery, particularly the change of the internal resistance of the battery under different states can be adjusted in real time by the internal resistance estimated by the model, so that the real-time description precision of the model is improved, and the aging state of the battery can be described and the parameters of the battery can be estimated. The experimental results verify the feasibility of the proposed model.
Disclosure of Invention
The invention aims to provide a combined simulation evaluation method for lithium battery health and state of charge, which not only can correctly provide the battery health state, but also can be self-adaptive to the battery aging state and keep higher simulation evaluation precision.
The invention provides a combined simulation and evaluation method for health and state of charge of a lithium battery, which adopts a battery equivalent circuit model, introduces Gaussian white noise in the relation between the state of charge and open-circuit voltage, estimates internal resistance as a variable in real time, and simultaneously links the internal resistance and capacity through the health state of the battery to update the real-time capacity of the battery, thereby ensuring that the model can be self-adaptive to the aging state of the battery and improving the estimation precision of the state of charge, and the method comprises the following specific steps:
(1) constructing an equivalent circuit model: and (3) carrying out pre-discharge test on the battery by adopting a lithium battery equivalent circuit model (a model given in the document [7 ]), calculating resistance and capacitance values in the model according to a measurement result, and verifying the accuracy of the model by using experimental data.
The detailed process is as follows:
document [7]]The equivalent circuit model of the lithium battery given in (1) is shown in fig. 1. In part (a), a capacitor C for capacity of the batterynCharacterised in that the current flowing into/out of the battery is represented by a controlled current source, such that CnThe increase and decrease of the voltage at two ends reflect the increase and decrease of the battery capacity, and 1V & SOC is used for representing CnThe voltage across; in part (b), controlled voltage Source OCV (SOC) is used to represent a non-linear mapping of battery SOC to open circuit voltage, R0Represents the equivalent ohmic internal resistance, R, of the battery1And C1And R2And C2Two RC networks are formed to reflect the dynamic characteristics of the battery with short time constant and long time constant.
Firstly, establishing an SOC-OCV relationship, fully charging a battery by adopting a constant-current and constant-voltage charging mode, discharging the battery by using a proper fixed discharge rate current (such as 0.5C-1C) after the battery is placed to a stable state, placing the battery after discharging for a period of time to obtain an open-circuit voltage in the current state, adopting a proper proportion (the placing time is recommended to be more than 5 times of the discharging time) between the discharging time and the placing time of the battery in each period, setting the sampling interval of the current and the voltage of the battery to be 1s, and continuously circulating to the discharging cut-off voltage of the battery; the battery is then charged using the same current in the same cycling mode as the discharging mode until the battery is charged to the charge cutoff voltage. Averaging is performed according to the measured charge and discharge data, so that a corresponding relationship between the state of charge and the open-circuit voltage of the battery can be obtained, as shown in fig. 2.
In addition, in consideration of the hysteresis characteristic of the battery, Gaussian white noise can be added into the relation curve for characterization.
Secondly, the battery is subjected to a hybrid pulse characteristic test, and resistance and capacitance values in an RC network representing the length and the short time constant of the battery can be calculated according to a discharge curve.
(2) And (3) constructing a state equation according to the equivalent circuit model: and selecting a proper variable in the model as a system state variable, and establishing an equation according to the model loop.
The detailed process is as follows:
from the equivalent circuit of fig. 1, it can be written that the battery model output voltage V is:
V(t+1)＝OCV(t)+I(t)R0(t)+VRC1(t)+VRC2(t) (1)
where t represents time, I (t) is the current through the cell at time t, which is positive during charging, negative during discharging, and VRC1And VRC2The dynamic characteristic of (c) can then be represented by:
Figure BDA0001560920380000031
Figure BDA0001560920380000032
document [12 ]]The research result shows that: equivalent internal resistance R of battery0Changes with the change in the SOC and state of health of the battery and is therefore different from what is reported in the literature, as in document 7]It will be considered herein as a state variable of the battery, as if it were a constant, and characterized by the following random walk model:
R0(t+1)＝R0(t)+r(t) (4)
in the formula, r (t) represents random white noise.
The controlled voltage Source Ocv (SOC) in fig. 1 reflects the mapping of the battery SOC to its open circuit voltage, and a typical charge-discharge process relationship is shown in fig. 2. As can be seen from fig. 2(a), the relationship between SOC and OCV during charging and discharging varies, i.e. OCV during charging and OCV during discharging are not the same value under the same SOC state [8 ]]This phenomenon is called a hysteresis phenomenon of the open circuit voltage. In literature reported studies, the relationship between SOC and OCV is usually characterized by taking the average value of OCV during charging and discharging[9]. FIG. 2(b) shows OCV by means of the average valueAV(SOC), the average of which is:
Figure BDA0001560920380000041
wherein the OCVup(SOC) and OCVdown(SOC) represents OCV values obtained by charging and discharging in fig. 2(a), respectively.
In order to describe the influence of the hysteresis phenomenon of charge and discharge OCVs on the battery characteristics, we will characterize the charge and discharge OCVs by introducing uncertainty describing the presence of the average value to the charge and discharge OCVs, based on the average OCV voltage, with white gaussian noise, whose variance can be determined from the maximum value of the deviation over the entire SOC range, to cover the possible deviation range, where we use VHRepresents, i.e.:
OCV(t)＝OCVav(t)+VH(t) (6)
as can be seen from FIG. 1(a), the capacitor CnThe voltage across is 1V · SOC, then the expression for SOC can be written as:
Figure BDA0001560920380000042
in formulae (1) to (7), the state variable is x ═ SOC, VRC1,VRC2,R0]Then, the equation of state describing the new model of the lithium battery with time-varying internal resistance and hysteresis can be written as:
Figure BDA0001560920380000043
V(t+1)＝OCVav(t)+VH(t)+I(t)R0(t)+VRC1(t)+VRC2(t)+v(t) (9)
where w (t) and v (t) represent state and observation noise, respectively.
(3) And (3) estimating the state equation (8) by using an unscented Kalman filtering algorithm, and updating the equivalent model in real time according to the relation between the estimated internal resistance and the capacity so as to ensure the real-time precision of the model.
The detailed process is as follows:
current capacity C of batterynThe SOH of the battery can be reflected, and the attenuation degree of the battery capacity with the recycling of the battery also indicates that the SOH of the battery is continuously reduced. SOH defined from the viewpoint of battery capacity is as follows[1]：
Figure BDA0001560920380000051
Wherein, CnowRepresents the maximum amount of electricity that the battery can discharge when fully charged after the battery ages; cnewIndicating the maximum amount of charge that the new battery can discharge when fully charged. According to the IEEE1188-1996 standard, when a battery is fully charged and its capacity is less than 80% of the rated capacity of the battery, the battery is considered to be at end of life and should be replaced. In this case, the SOH represented by the formula (10)CThe variation range of (1) to (0.8), 1 representing that the battery is a new battery, and 0.8 representing that the battery has aged to the end of its life.
Formula (10) indicates that: in the case where SOH is known, the current battery capacity can be obtained by equation (10). Further, SOH can also be defined from the viewpoint of internal resistance as follows[13]：
Figure BDA0001560920380000052
From document [13 ]]The reported results show that the internal resistance of the battery increases as the battery ages at the same temperature and at the same SOC. The resistances in this pattern (11) should all be values measured at the same temperature and SOC, where R is0,EOLThe internal resistance of the battery when the battery is aged to the end-of-life state is expressed, and according to the IEEE1188-1996 standard, the internal resistance is considered to be the internal resistance when the maximum dischargeable electric quantity of the battery is attenuated to 80% of the maximum dischargeable electric quantity of a new battery, R0,newThen represents the internal resistance of the new battery, R0,nowRepresenting the internal resistance of the current battery. As can be seen from the formula (11), SOHRIs 1-0, i.e., 1 represents that the battery is a new battery and 0 represents that the battery has aged to its end-of-life state.
From the above analysis, it can be seen that as the battery ages, the battery capacity CnAnd internal resistance R0Changes will occur. And in the equation of state of the formula (8), R0Has been characterized using a random walk equation, but capacity CnVariations of (a) are not described. For updating the capacity C in real timenTo make the model describing the battery more accurate, we will give the updated capacity C belownThe method of (1).
The results of document [14] show that: the following linear relationship exists between the battery capacity fade and the battery internal resistance:
Cfnow(％)＝kR0,now+b (12)
wherein, Cfnow(%) represents the percentage of the current maximum dischargeable charge decay, i.e.:
Figure BDA0001560920380000061
this formula (12) can be substituted for the formula (11):
Figure BDA0001560920380000062
wherein, let Cnew-Cnew(kR0,EOL+b)＝CEOLFor the battery to reach the end of lifeThe maximum dischargeable electric quantity in the state indicates that:
Figure BDA0001560920380000063
and the initial capacity and internal resistance of the battery, and the end-of-life capacity and internal resistance are known values, the updated capacity can be found from equation (15):
Figure BDA0001560920380000064
let R in formula (8)0(t)＝R0,nowThen, there are:
Figure BDA0001560920380000065
in the formula
Figure BDA0001560920380000066
The expression definition means that the new models (8), (9) and (17) of the present invention can simulate the battery according to the state of use (health or aging) of the battery.
The overall flow of the simulation evaluation method (new model) for combining the lithium battery health and the state of charge provided by the invention is shown in fig. 3. Time-varying internal resistance and hysteresis characteristics are introduced into an original circuit equivalent model, a random walk model is used for representing the internal resistance, and white Gaussian noise is used for representing the uncertainty of an SOC-OCV curve. The internal resistance value estimated by the random walk model is correlated with the state of health of the battery, and the updated internal resistance value can be used for updating the battery capacity parameter for the model. Finally, we have built a new model for battery state of charge estimation and state of health estimation. Through the updated internal resistance value of the model and the battery capacity, the real-time description precision of the model can be improved, the health state parameters of the battery can be provided, and the battery can meet the working requirements of the system. The experimental results show that: the charge state estimation result based on the new model can reach high precision, and most results can be kept in an error range of 3%; in addition, under the condition of battery aging, the capacity updating can be close to the true value with higher precision, the battery health state is provided for users, and under the condition of battery aging, the state of charge estimation still has higher precision.
Drawings
Fig. 1 is a diagram of an equivalent circuit model employed.
Fig. 2 is a SOC-OCV relationship diagram. Wherein, the two curves in (a) are SOC-OCV relation curves during charging and discharging respectively, and the curve in (b) is averaged according to the charging and discharging relation curves to obtain a final SOC-OCV curve.
FIG. 3 is a flow chart of the overall model state estimation.
Fig. 4 shows the results of model validation, showing the estimated and measured battery voltage values.
Fig. 5 is a graph of the absolute error of the battery voltage estimate, as a result of model validation.
Fig. 6 shows the model verification results, showing the estimated value and the true value of the battery SOC.
Fig. 7 is a model verification result showing an absolute error of the battery SOC estimation.
FIG. 8 is a model validation result, as a percentage error of battery capacity estimation.
Fig. 9 is a result of verification when the battery is aged to SOH of 91%. Wherein, the comparison result of the estimated value of the SOC of the battery and the actual value is shown in (a), and the percentage error of the estimated value of the battery capacity is shown in (b).
Detailed Description
1. Constructing equivalent circuit model
In the test experiment, a lithium ion polymer battery cell LGABF1L18650 battery with rated capacity of 3350mAh and rated voltage of 3.7V was used. The model parameters need to be identified by some charge-discharge tests. All experiments were performed at 25 degrees celsius.
Firstly, establishing an SOC-OCV relationship, fully charging a battery by adopting a constant-current and constant-voltage charging mode, discharging the battery by using a current with a discharge rate of 0.6C after standing for 1h, discharging the battery for 120s in each period, standing for 720s, and continuously circulating to a battery discharge cut-off voltage, wherein the sampling interval of the current and the voltage of the battery is 1 s; the battery is then charged using the same current in the same cycling mode as the discharging mode until the battery is charged to the charge cutoff voltage. Averaging is performed according to the measured charge and discharge data, so that a corresponding relationship between the state of charge and the open-circuit voltage of the battery can be obtained, as shown in fig. 2. The relationship between SOC and OCV is constructed by piecewise linear fitting of the curve in fig. 2, and specific fitting parameters are shown in table 1. In addition, in consideration of hysteresis characteristics existing in the battery, white gaussian noise with a standard deviation of 0.02 may be added to the relationship curve for characterization.
Next, the battery was subjected to a hybrid pulse characteristic test, reference [6 ]][9]From the discharge curve, the resistance and capacitance values in the RC network representing the battery length and short time constant can be calculated: r1＝0.001Ω，C1＝618F，R2＝0.0257Ω，C2＝707.7F。
2. Constructing equations of state
Let the state variable be x ═ SOC, VRC1,VRC2,R0]And (3) substituting the resistance and capacitance measured in the step (1) into the equations (8) and (9) to construct a state equation.
3. State estimation and real-time update equivalent model
Aiming at the state equation constructed in the step 2, the unscented Kalman filtering algorithm is adopted to estimate the unscented Kalman filtering algorithm, the internal resistance estimated each time is linked with the battery capacity through the health state, and the capacity is estimated through the formula (17). The estimation result of each time can not only provide the battery health information, but also update the battery model in real time, and ensure the precision of the model in various states.
Fig. 4 and 5 are results of comparison of measured values of the terminal voltage of the battery with the estimated values of the model, and it can be seen from fig. 4 that the estimated voltage curve fits well to the actually measured curve, and the absolute error of the test thereof is shown in fig. 5, and it can be seen therefrom that the error between the two is always kept within a very small range, whereby it can be seen that the estimated voltage has a high accuracy; FIGS. 6 and 7 are comparison results of the real value of the SOC of the battery calculated by the modified ampere-hour integration method and the estimated value of the model[6]Estimated curves in FIG. 6The actual value curve is well fitted, the absolute error of the test is shown in fig. 7, and it can be seen that the difference between the two is kept in a small range, the estimation error is mostly kept within 3%, and it can be seen that the SOC estimation has high accuracy. FIG. 8 shows the results of a percentage error map for updating capacity with estimated internal resistance values when only SOC > 0.2 is used in updating Cn, since the internal resistance increases exponentially when SOC < 0.2. The capacity of the experimental battery is 3350mAh, and the percentage error of the estimation result is within 5 percent.
Fig. 9 shows the test results when the battery was aged to 91% SOH. FIG. 9(a) is a comparison of the true value of the battery SOC with the model estimated value; fig. 9(b) gives the percentage error map result for updating the capacity with the estimated internal resistance. It can be seen from the results that the model still maintained good performance in the aged state.
Table 1: piecewise fitting coefficient of SOC-OCV curve
Figure BDA0001560920380000081
Reference to the literature
[1]Lu L，Han X，Li J，et al.A review on the key issues for lithium-ionbattery management in electric vehicles[J].Journal ofPower Sources，2013，226(3)：272-288.
[2]Caumont O，Moigne P L，Rombaut C，et al.Energy gauge for lead-acidbatteries in electric vehicles[J].Energy Conversion IEEE Transactions on，2000，15(3)：354-360.
[3]Dai H，Sun Z，Wei X.Online SOC Estimation of High-power Lithium-ionBatteries Used on HEVs[C]//IEEE International Conference on VehicularElectronics and Safety.IEEE，2006：342-347.
[4]Rodrigues S,Munichandraiah N,Shukla A K.A review of state-of-charge indication of batteries by means of a.c.impedance measurements[J].Journal of Power Sources,2000,87(1–2):12-20.
[5]Domenico D D,Fiengo G,Stefanopoulou A.Lithium-ion battery state ofcharge estimation with a Kalman Filter based on an electrochemical model[C]//IEEE International Conference on Control Applications.IEEE,2008:702-707.
[6]Kim I S.The novel state of charge estimation method for lithiumbattery using sliding mode observer[J].Journal of Power Sources,2006,163(1):584-590.
[7]Chen M,Rincon-Mora G A.Accurate electrical battery model capableof predicting runtime and I-V performance[J].IEEE Transactions on EnergyConversion,2006,21(2):504-511.
[8]Roscher M A,Bohlen O,Vetter J.OCV Hysteresis in Li-Ion Batteriesincluding Two-Phase Transition Materials[J].International Journal ofElectrochemistry,2011,(2011-05-29),2011,2011(6).
[9]Baronti F,Zamboni W,Femia N,et al.Experimental analysis of open-circuit voltage hysteresis in lithium-iron-phosphate batteries[C]//IndustrialElectronics Society,IECON 2013-,Conference of the IEEE.IEEE,2013:6728-6733.
[10]NING G,HARAN B,POPOV B N.Capacity fade study of lithium-ionbatteries cycled at high discharge rates[J]Journal of Power Sources,2003,117,(1–2),160–169[J].2004(5):329.
[11]Ramadass P,Haran B,White R,et al.Mathematical modeling of thecapacity fade of Li-ion cells[J].Journal of Power Sources,2003,123(2):230-240.
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Claims (1)

1. A joint simulation evaluation method for the health and the state of charge of a lithium battery is characterized in that a battery equivalent circuit model is adopted, Gaussian white noise is introduced into the relation between the state of charge and open-circuit voltage, internal resistance is used as variable to estimate in real time, and the internal resistance and the capacity are linked through the health state of the battery to update the real-time capacity of the battery, so that the model can be self-adaptive to the aging state of the battery, and the estimation precision of the state of charge is improved; the state conversion in the model is only related to the last estimated value and the current observed value, so that the method has good robustness and is suitable for estimation of any state; the method comprises the following specific steps:
(1) constructing an equivalent circuit model: adopting a lithium battery equivalent circuit model to perform a pre-discharge test on the battery, calculating resistance and capacitance values in the model according to a measurement result, and verifying the accuracy of the model by using experimental data;
(2) and (3) constructing a state equation according to the equivalent circuit model: selecting variables in the model as system state variables, and establishing an equation according to the model loop;
(3) estimating a state equation by using an unscented Kalman filtering algorithm, linking the estimated internal resistance with the capacity, and updating the equivalent model in real time to ensure the real-time precision of the model;
the process of the step (1) is as follows:
in the equivalent circuit model of lithium battery, the capacity of the battery uses the electric capacity CnCharacterised in that the current flowing into/out of the battery is represented by a controlled current source, such that CnThe increase and decrease of the voltage at both ends reflect the increase and decrease of the battery capacity, and C is represented by 1 V.SOCnThe voltage at two ends and the SOC represent the charge state of the battery and are defined as the ratio of the residual electric quantity of the battery to the full electric quantity of the battery; controlled voltage Source OCV (SOC) is used to represent a non-linear mapping of battery SOC to open circuit voltage OCV, R0Represents the equivalent ohmic internal resistance, R, of the battery1And C1And R2And C2Form aThe two RC networks are respectively used for reflecting the dynamic characteristics of the short-time constant and the long-time constant of the battery;
firstly, establishing an SOC-OCV relationship, fully charging a battery by adopting a constant-current and constant-voltage charging mode, discharging the battery by using proper fixed discharge rate current after the battery is placed to a stable state, placing the battery for a period of time after discharging to obtain open-circuit voltage in the current state, adopting proper proportion between the time of discharging and placing the battery in each period, wherein the sampling interval of the current and the voltage of the battery is 1s, and continuously circulating to the discharge cut-off voltage of the battery; averaging according to the measured charging and discharging data to obtain a corresponding relation between the state of charge and the open-circuit voltage of the battery; adding Gaussian white noise into the relation curve for characterization;
then, performing hybrid power pulse characteristic test on the battery, and calculating resistance and capacitance values in an RC network representing the length and short time constant of the battery according to a discharge curve;
the specific process of the step (2) is as follows:
according to the lithium battery equivalent circuit model, the output voltage V is as follows:
V(t+1)＝OCV(t)+I(t)R0(t)+VRC1(t)+VRC2(t) (1)
where t represents time, I (t) is the current through the cell at time t, which is positive during charging, negative during discharging, and VRC1And VRC2Is represented by the following formula:
Figure FDA0002527869030000021
Figure FDA0002527869030000022
R0the equivalent internal resistance of the battery changes along with the change of the SOC and the state of health of the battery, the equivalent internal resistance is regarded as a state variable of the battery, and the equivalent internal resistance is characterized by the following random walk model:
R0(t+1)＝R0(t)+r(t) (4)
wherein r (t) represents random white noise;
in the lithium battery equivalent circuit model, a controlled voltage Source OCV (SOC) reflects the mapping from the battery SOC to the open-circuit voltage, and for the hysteresis phenomenon of the open-circuit voltage, the relation between the SOC and the OCV is represented by taking the average value of the OCVs in the charging and discharging processes, wherein the average value is as follows:
Figure FDA0002527869030000023
wherein the OCVup(SOC) and OCVdown(SOC) represents OCV values obtained by charging and discharging, respectively;
the uncertainty of this average value to the charge and discharge OCV is characterized by white gaussian noise on the basis of the average OCV voltage, the variance of this noise being determined from the maximum value of the deviation over the entire SOC range, to cover the possible deviation range, here by VHRepresents, i.e.:
OCV(t)＝OCVav(t)+VH(t) (6)
capacitor CnThe voltage across is 1V · SOC, then the expression for SOC is written as:
Figure FDA0002527869030000024
in formulae (1) to (7), the state variable is x ═ SOC, VRC1,VRC2,R0]Then, the state equation describing the new model of the lithium battery with time-varying internal resistance and hysteresis is:
Figure FDA0002527869030000031
V(t+1)＝OCVav(t)+VH(t)+I(t)R0(t)+VRC1(t)+VRC2(t)+v(t) (9)
wherein w (t) and v (t) represent state and observation noise, respectively;
the specific process of the step (3) is as follows:
current capacity C of batterynReflecting the state of health SOH of the battery, the SOH defined from a battery capacity perspective is as follows:
Figure FDA0002527869030000032
wherein, CnowRepresents the maximum amount of electricity that the battery can discharge when fully charged after the battery ages; cnewThe maximum electric quantity which can be discharged when the new battery is fully charged is represented;
SOH is defined from an internal resistance perspective as follows:
Figure FDA0002527869030000033
wherein R is0,EOLIndicating the internal resistance of the battery as it ages to an end-of-life state;
as the battery ages, the battery capacity CnAnd internal resistance R0Will change; in the equation of state of the formula (8), R0Has been characterized using a random walk equation, and the update capacity C is given belownThe method of (1);
the following linear relationship exists between the battery capacity fade and the battery internal resistance:
Cfnow(％)＝kR0,now+b (12)
wherein, Cfnow(%) represents the percentage of the current maximum dischargeable charge decay, i.e.:
Figure FDA0002527869030000034
substituting formula (12) for formula (11) to obtain:
Figure FDA0002527869030000035
wherein, let Cnew-Cnew(kR0,EOL+b)＝CEOLFor the battery to reach the lifeThe maximum dischargeable electric quantity in the end state is represented as:
Figure FDA0002527869030000041
and the initial capacity and internal resistance of the battery, and the capacity and internal resistance at the end of life are known values, the updated capacity is obtained by equation (15):
Figure FDA0002527869030000042
let R in formula (8)0(t)＝R0,nowThen, there are:
Figure FDA0002527869030000043
in the formula
Figure FDA0002527869030000044
By means of the representation definition, the battery can be simulated according to the using state of the battery through the model equations (8), (9) and (17).
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